There are in the art a number of flexible guide wires used in medical applications. Exemplary such devices are shown in U.S. Pat. Nos. 3,789,841, 4,538,622, 4,545,390, 4,721,117, and 4,884,579, all of which are hereby incorporated by reference. Some such devices, including those shown in U.S. Pat. Nos. 3,789,841, 4,721,117 and 4,884,579, include a plastic (e.g., Teflon) covering that surrounds at least a portion of the guide wire. In some of these devices, a constant diameter Teflon jacket surround the uniform diameter portion of the core wire; in some, a more tip portion is coated with Teflon or covered with a polymeric tube that is in turn Teflon coated; in some, the Teflon covering is sprayed on. The sprayed coatings are often are somewhat rough and prone to peeling; and both they and tubular sleeves typically undesirably increase the overall diameter of at least some portions of the overall guide wire.